Question

Apply the Pythagorean Theorem to find the length between (2, 5)
and (7, 3)
. Round your answer to the nearest hundredth, if necessary.(1 point)
Responses

2.65
2.65

4.58
4.58

29
29

5.39

Answer 1

To find the distance between the points (2, 5) and (7, 3) using the Pythagorean Theorem, we can use the distance formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

where \((x_1, y_1)\) is the first point and \((x_2, y_2)\) is the second point. Here, \((x_1, y_1) = (2, 5)\) and \((x_2, y_2) = (7, 3)\).

Now, we can substitute the coordinates into the formula:

\[
d = \sqrt{(7 - 2)^2 + (3 - 5)^2}
\]

Calculate the differences:

\[
= \sqrt{(5)^2 + (-2)^2}
\]

\[
= \sqrt{25 + 4}
\]

\[
= \sqrt{29}
\]

Now, calculating \(\sqrt{29}\):

\[
\sqrt{29} \approx 5.385
\]

Rounding this to the nearest hundredth gives us:

\[
d \approx 5.39
\]

Thus, the length between the points (2, 5) and (7, 3) is approximately **5.39**.